A Study on Distortion Estimation Based on Image Gradients

Image noise is a variation of uneven pixel values that occurs randomly. A good estimation of image noise parameters is crucial in image noise modeling, image denoising, and image quality assessment. To the best of our knowledge, there is no single estimator that can predict all noise parameters for multiple noise types. The first contribution of our research was to design a noise data feature extractor that can effectively extract noise information from the image pair. The second contribution of our work leveraged other noise parameter estimation algorithms that can only predict one type of noise. Our proposed method, DE-G, can estimate additive noise, multiplicative noise, and impulsive noise from single-source images accurately. We also show the capability of the proposed method in estimating multiple corruptions.

The Influence of Noise on the Exact Solutions of the Stochastic Fractional-Space Chiral Nonlinear Schrödinger Equation

In this paper, we consider the stochastic fractional-space Chiral nonlinear Schrödinger equation (S-FS-CNSE) derived via multiplicative noise. We obtain the exact solutions of the S-FS-CNSE by using the Riccati equation method. The obtained solutions are extremely important in the development of nuclear medicine, the entire computer industry and quantum mechanics, especially in the quantum hall effect. Moreover, we discuss how the multiplicative noise affects the exact solutions of the S-FS-CNSE. This equation has never previously been studied using a combination of multiplicative noise and fractional space.

Weak Convergence Rates for Spatial Spectral Galerkin Approximations of Semilinear Stochastic Wave Equations with Multiplicative Noise

Stochastic wave equations appear in several models for evolutionary processes subject to random forces, such as the motion of a strand of DNA in a liquid or heat flow around a ring. Semilinear stochastic wave equations can typically not be solved explicitly, but the literature contains a number of results which show that numerical approximation processes converge with suitable rates of convergence to solutions of such equations. In the case of approximation results for strong convergence rates, semilinear stochastic wave equations with both additive or multiplicative noise have been considered in the literature. In contrast, the existing approximation results for weak convergence rates assume that the diffusion coefficient of the considered semilinear stochastic wave equation is constant, that is, it is assumed that the considered wave equation is driven by additive noise, and no approximation results for multiplicative noise are known. The purpose of this work is to close this gap and to establish essentially sharp weak convergence rates for spatial spectral Galerkin approximations of semilinear stochastic wave equations with multiplicative noise. In particular, our weak convergence result establishes as a special case essentially sharp weak convergence rates for the continuous version of the hyperbolic Anderson model. Our method of proof makes use of the Kolmogorov equation and the Hölder-inequality for Schatten norms.